This type of hardware is cheap, economical, and gets you up and running in a
few minutes. The downside is that you can't do much else with these things.
Yes, there are many custom firmwares, which allow you more freedom, but the
hardware is often the limiting factor.

convert a regular PC into a router

If you want more than just routing, building your own router using a(n) (old)
PC is the preferred course of action. The downside is that a PC often uses
more 'juice' than an embedded device.

However, those new Atom-based PC's may be a very nice option. Just add a
second network card, though an USB-port or a low profile PCI card
and you have something far more flexible than an embedded router.

convert a laptop into a router

It sounds a bit strange and silly at first to use a laptop as a router, but it
makes sense when you think of it.

It is economical in terms of power usage

It has a build-in UPS called a 'battery'

It has a build-in screen and keyboard

All these things are an advantage regarding option 2.

Nowadays you can have a netbook for only 300 euros. It is more expensive than
an embedded device, but almost as economical and provides much more
performance and flexibility.

I've been running an old laptop as a router for 6 months without problems.
Unfortunately, the disk died due to old age, but that can happen to any
computer. I'm now running an old mac mini intel machine as a router.